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Condensed matter physics, area laws & LQG?

  1. May 18, 2017 #376

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    https://arxiv.org/abs/1705.06283
    Classical Spacetimes as Amplified Information in Holographic Quantum Theories
    Yasunori Nomura, Pratik Rath, Nico Salzetta
    (Submitted on 17 May 2017)
    We argue that classical spacetimes represent amplified information in the holographic theory of quantum gravity. In general, classicalization of a quantum system involves amplification of information at the cost of exponentially reducing the number of observables. In quantum gravity, the geometry of spacetime must be the analogously amplified information. Bulk local semiclassical operators probe this information without disturbing it; these correspond to logical operators acting on code subspaces of the holographic theory. From this viewpoint, we study how bulk local operators may be realized in a holographic theory of general spacetimes, which includes AdS/CFT as a special case, and deduce its consequences. In the first half of the paper, we ask what description of the bulk physics is provided by a holographic state dual to a semiclassical spacetime. In particular, we analyze what portion of the bulk can be reconstructed in the holographic theory. The analysis indicates that when a spacetime contains a quasi-static black hole inside a holographic screen, the theory provides a description of physics as viewed from the exterior (though the interior information is not absent). In the second half, we study how and when a semiclassical description emerges in the holographic theory. We find that states representing semiclassical spacetimes are non-generic in the holographic Hilbert space; in particular, microstates for a semiclassical spacetime do not form a Hilbert space. When there are a significant number of independent microstates, semiclassical operators must be given state-dependently. We elucidate this point using the stabilizer formalism and tensor network models. We also argue that semiclassical states, albeit exponentially rare in the Hilbert space, can be dynamically selected under time evolution. Finally, we discuss implications of the present picture for the black hole interior.


    https://arxiv.org/abs/1705.06711
    Local Lorentz covariance in finite-dimensional Local Quantum Physics
    Matti Raasakka
    (Submitted on 18 May 2017)
    We show that local Lorentz covariance arises canonically as the group of transformations between local thermal states in the framework of Local Quantum Physics, given the following three postulates: (i) Local observable algebras are finite-dimensional. (ii) Minimal local observable algebras are isomorphic to M2(C), the observable algebra of a single qubit. (iii) The vacuum restricted to any minimal local observable algebra is thermal. The derivation reveals a new and surprising relation between spacetime structure and local quantum states. In particular, we show how local restrictions of the vacuum can determine the connection between different local inertial reference frames.
     
    Last edited: May 19, 2017
  2. Jun 24, 2017 #377

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    https://arxiv.org/abs/1706.07056
    Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
    Pawel Caputa, Nilay Kundu, Masamichi Miyaji, Tadashi Takayanagi, Kento Watanabe
    (Submitted on 21 Jun 2017)
    We propose an optimization procedure for Euclidean path-integrals that evaluate CFT wave functionals in arbitrary dimensions. The optimization is performed by minimizing certain functional, which can be interpreted as a measure of computational complexity, with respect to background metrics for the path-integrals. In two dimensional CFTs, this functional is given by the Liouville action. We also formulate the optimization for higher dimensional CFTs and, in various examples, find that the optimized hyperbolic metrics coincide with the time slices of expected gravity duals. Moreover, if we optimize a reduced density matrix, the geometry becomes two copies of the entanglement wedge and reproduces the holographic entanglement entropy. Our approach resembles a continuous tensor network renormalization and provides a concrete realization of the proposed interpretation of AdS/CFT as tensor networks. The present paper is an extended version of our earlier report arXiv:1703.00456 and includes many new results such as evaluations of complexity functionals, energy stress tensor, higher dimensional extensions and time evolutions of thermofield double states.

    https://arxiv.org/abs/1706.07143
    Black Hole Information Revisited
    Andrew Strominger
    (Submitted on 22 Jun 2017)
    We argue that four-dimensional black hole evaporation inevitably produces an infinite number of soft particles in addition to the thermally distributed `hard' Hawking quanta, and moreover that the soft and hard particles are highly correlated. This raises the possibility that quantum purity is restored by correlations between the hard and soft radiation, while inclusive measurements which omit the soft radiation observe the thermal Hawking spectrum. In theories whose only stable particle is the graviton, conservation laws are used to argue that such correlations are in principle sufficient for the soft gravitons to purify the hard thermal ones.

    https://arxiv.org/abs/1706.07424
    Loss of locality in gravitational correlators with a large number of insertions
    Sudip Ghosh, Suvrat Raju
    (Submitted on 22 Jun 2017)
    We review lessons from the AdS/CFT correspondence that indicate that the emergence of locality in quantum gravity is contingent on considering observables with a small number of insertions. Correlation functions where the number of insertions scales with a power of the central charge of the CFT are sensitive to nonlocal effects in the bulk theory, which arise from a combination of the effects of the bulk Gauss law and a breakdown of perturbation theory. To examine whether a similar effect occurs in flat space, we consider the scattering of massless particles in the bosonic string and the superstring in the limit where the number of external particles, n, becomes very large. We use estimates of the volume of the Weil-Petersson moduli space of punctured Riemann surfaces to argue that string amplitudes grow factorially in this limit. We verify this factorial behaviour through an extensive numerical analysis of string amplitudes at large n. Our numerical calculations rely on the observation that, in the large n limit, the string scattering amplitude localizes on the Gross-Mende saddle points, even though individual particle energies are small. This factorial growth implies the breakdown of string perturbation theory for n∼(Mpl/E)d−2 in d dimensions where E is the typical individual particle energy. We explore the implications of this breakdown for the black hole information paradox. We show that the loss of locality suggested by this breakdown is precisely sufficient to resolve the cloning and strong subadditivity paradoxes.
     
  3. Jul 1, 2017 #378

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    https://arxiv.org/abs/1706.09617
    Entanglement entropy, the Einstein equation and the Sparling construction
    Mahdi Godazgar
    (Submitted on 29 Jun 2017)
    We relate the recent derivation of the linearised Einstein equation on an AdS background from holographic entanglement entropy arguments to the Sparling construction: we derive the differential form whose exterior derivative gives the Einstein equation from the Sparling formalism. We develop the study of perturbations within the context of the Sparling formalism and find that the Sparling form vanishes for linearised perturbations on flat space.
     
  4. Nov 20, 2017 #379

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    https://arxiv.org/abs/1711.05967
    A Renormalizable SYK-type Tensor Field Theory
    Joseph Ben Geloun, Vincent Rivasseau
    (Submitted on 16 Nov 2017)
    In this paper we introduce a simple field theoretic version of the Carrozza-Tanasa-Klebanov-Tarnopolsky (CTKT) "uncolored" holographic tensor model. It gives a more familiar interpretation to the previously abstract modes of the SYK or CTKT models in terms of momenta. We choose for the tensor propagator the usual Fermionic propagator of condensed matter, with a spherical Fermi surface, but keep the CTKT interactions. Hence our field theory can also be considered as an ordinary condensed matter model with a non-local and non-rotational invariant interaction. Using a multiscale analysis we prove that this field theory is just renormalizable to all orders of perturbation theory in the ultraviolet regime.
     
  5. Dec 3, 2017 #380

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    https://arxiv.org/abs/1711.08482
    AdS2 holography and the SYK model
    Gábor Sárosi
    (Submitted on 22 Nov 2017)
    These are lecture notes based on a series of lectures presented at the XIII Modave Summer School in Mathematical physics aimed at PhD students and young postdocs. The goal is to give an introduction to some of the recent developments in understanding holography in two bulk dimensions, and its connection to microscopics of near extremal black holes. The first part reviews the motivation to study, and the problems (and their interpretations) with holography for AdS2 spaces. The second part is about the Jackiw-Teitelboim theory and nearly-AdS2 spaces. The third part introduces the Sachdev-Ye-Kitaev model, reviews some of the basic calculations and discusses what features make the model exciting.
     
  6. Dec 11, 2017 #381

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    https://arxiv.org/abs/1712.02803
    Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
    ChunJun Cao, Sean M. Carroll
    (Submitted on 7 Dec 2017)
    We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how Radon transforms can be used to convert this data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.
     
  7. Jan 17, 2018 #382

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    https://arxiv.org/abs/1711.10854
    A Review of the Holographic Relation between Linearized Gravity and the First Law of Entanglement Entropy
    Rasmus Jaksland
    (Submitted on 29 Nov 2017)
    This thesis reviews the conjectured holographic relation between entanglement and gravity due to Mark van Raamsdonk and collaborators. It is accounted how the linearized Einstein equations both with and without matter in a d+1-dimensional AdS background can be derived from the first law of entanglement entropy in a d-dimensional CFT. This derivation builds on the Ryu-Takayanagi formula that relates entanglement entropy for CFT subsystems to extremal surfaces in the AdS bulk. The relation between gravity and entanglement is also corroborated by a qualitative investigation of the duality between the thermofield double state and the maximally extended AdS/Schwarzschild black hole using the Bekenstein-Hawking formula. Furthermore, this qualitative argument is generalized to generic CFT states with a classical spacetime dual using the Ryu-Takayanagi. The thesis also reviews the most relevant prerequisites for this holographic relation between gravity and entanglement: Anti-de Sitter spacetime, entanglement and entanglement entropy, gauge/gravity duality, the Ryu-Takayanagi formula, and linearized gravity.

    https://arxiv.org/abs/1801.05289
    Space-time random tensor networks and holographic duality
    Xiao-Liang Qi, Zhao Yang
    (Submitted on 16 Jan 2018)
    In this paper we propose a space-time random tensor network approach for understanding holographic duality. Using tensor networks with random link projections, we define boundary theories with interesting holographic properties, such as the Renyi entropies satisfying the covariant Hubeny-Rangamani-Takayanagi formula, and operator correspondence with local reconstruction properties. We also investigate the unitarity of boundary theory in spacetime geometries with Lorenzian signature. Compared with the spatial random tensor networks, the space-time generalization does not require a particular time slicing, and provides a more covariant family of microscopic models that may help us to understand holographic duality.
     
  8. Jun 9, 2018 #383

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    https://arxiv.org/abs/1802.01040
    TASI Lectures on the Emergence of the Bulk in AdS/CFT
    Daniel Harlow
    (Submitted on 3 Feb 2018 (v1), last revised 22 Feb 2018 (this version, v2))
    These lectures review recent developments in our understanding of the emergence of local bulk physics in AdS/CFT. The primary topics are sufficient conditions for a conformal field theory to have a semiclassical dual, bulk reconstruction, the quantum error correction interpretation of the correspondence, tensor network models of holography, and the quantum Ryu-Takayanagi formula.
     
  9. Jul 16, 2018 at 5:51 PM #384

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    https://physics.aps.org/articles/v11/67
    Q&A: Searching for the Quantumness of Gravity
    June 29, 2018• Physics 11, 67
    Brian Swingle believes that quantum entanglement could explain the nature of spacetime—an idea that could lead to a quantum theory of gravity.
     
  10. Jul 18, 2018 at 3:17 AM #385

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